1 4D-animated representation:
1.1 Ocneanu’s Octacube Animation
Ocneanu’s octacube animation and existing three-dimensional solid sculpture employed for the
animation were described as follows.
Description of the ‘Octacube’: “The subject of the projection is a regular 4-dimensional solid of
intermediate complexity, which Ocneanu calls an “octacube.” It has 24 vertices, 96 edges and 96
triangular faces, which enclose 24 three-dimensional “rooms.” Windows cut in faces allow the
viewer to see within the structure, the same way that a window in a cubic room opens to the inside
of the cube. Physically, the sculpture is a giant puzzle of 96 triangular pieces cut from stainless
steel and bent into spherical shape”; (a quote attributed to the octacube’s inventor, Professor
Adrian Ocneanu).
Note: The following is an example of a hand-drawn ‘mathematical diagram’ by Alex Grothendieck
around 1970 (perhaps a ‘dessin d’enfants’ ? , or is it a 2D representation of an n-dimensional real
space by Alex’s ‘doodle’ drawing ?)
*Click on the dessin d’enfants, blue text above, to link to the web site that has the
downloadable images.
